if True:
    import numpy as np
    import pandas as pd

    # Add lab library
    import sys
    sys.path.insert(0, '/home/trevormjs/Documents/Science/APL/Lab')

    #---------------------------------------------------------------------#
    #                        matplotlib plotting                          #
    #---------------------------------------------------------------------#
    import matplotlib.pyplot as plt
    import matplotlib as mpl
    from jupyterthemes import jtplot
    from Helper.plotting import my_graph
    # Edit the font, font size, and axes width
    # mpl.rcParams['font.family'] = 'Avenir'
    plt.rcParams['font.size'] = 24
    plt.rcParams['axes.linewidth'] = 2
    jtplot.style(theme='monokai', context='notebook', ticks=False, grid=False)

    #---------------------------------------------------------------------#
    #                           bokeh plotting                            #
    #---------------------------------------------------------------------#
    from bokeh.plotting import figure, show, output_notebook
    from bokeh.themes import Theme
    from bokeh.io import curdoc, export_png
    from bokeh.models import (Range1d, Label, ColumnDataSource, LabelSet,
                              Legend)
    from Helper.plotting import style
    output_notebook()
    # curdoc().theme = Theme(filename="../Helper/theme.yml")

    #---------------------------------------------------------------------#
    #                       error and unit handling                       #
    #---------------------------------------------------------------------#
    from uncertainties import ufloat
    import Helper.numbers as nu
    from Helper.record import Measurement, Unit

    %load_ext autoreload
    %autoreload 2

Loading BokehJS ...

pd.set_option('plotting.backend', 'pandas_bokeh')

Basic FFT

1, Sine wave

x = np.linspace(0, .1, 2048)
y = np.sin(2*np.pi*100*x)
window = np.hamming(len(x))
coefs = np.fft.fft(window*y)
freqs = np.fft.fftfreq(y.shape[0], d=x[1]-x[0])

1/(x[1]-x[0])

20470.0

fig = figure(width=600, height=400)
fig.line(x, y, line_width=3)#, color = 'blue')
# fig.line(x, np.hamming(y.shape[0]), color = 'red')
# fig.line(x, y*window, color = 'purple')
# fig.x_range = Range1d(80, 120)
style(fig, 'x (s)','y')
show(fig)
export_png(fig, filename = '../Images/l5_A_1a.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_A_1a.png'

fig = figure(width=600, height=400)
fig.line(np.fft.fftshift(freqs), np.fft.fftshift(np.abs(coefs)), line_width=3)
fig.x_range = Range1d(70, 130)
style(fig, 'Frequency (Hz)', 'Amplitude')
show(fig)
export_png(fig, filename = '../Images/l5_A_1b.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_A_1b.png'

nu.halfmax(np.abs(coefs), [coefs.argmax()])[0]*(freqs[1]-freqs[0])

array([17.42189888])

freqs[1]-freqs[0]

9.9951171875

freqs.max()

10225.0048828125

1/(x[1]-x[0])

2047.0

2, Larger number of cycles

x = np.linspace(0, 1, 2048)
y = np.sin(2*np.pi*100*x)
window = np.hamming(len(x))
coefs_2 = np.fft.fft(window*y)
freqs_2 = np.fft.fftfreq(y.shape[0], d=x[1]-x[0])

fig = figure(width=600, height = 400)
fig.line(x, y, line_width=3)
# fig.line(x, np.hamming(y.shape[0]), color = 'red')
# fig.line(x, y*window, color = 'purple')
# fig.x_range = Range1d(80, 120)
style(fig, 'x (s)','y')
# fig.yaxis.major_label_orientation = 'horizontal'
show(fig)

nu.halfmax(np.abs(coefs_2), [coefs_2.argmax()])[0]*(freqs_2[1]-freqs_2[0])

array([1.75386876])

freqs_2[1]-freqs_2[0]

0.99951171875

freqs_2.max()

1022.50048828125

1/(x[1]-x[0])

2047.0

fig = figure(height=400, width=600)
fig.line(np.fft.fftshift(freqs),
         np.fft.fftshift(
             np.abs(coefs))/np.abs(coefs).max(),
         line_width=3,
         legend_label='0.1 Seconds')
fig.line(np.fft.fftshift(freqs_2),
         np.fft.fftshift(
             np.abs(coefs_2))/np.abs(coefs_2).max(),
         line_width=3,
         color='firebrick',
         legend_label='1.0 Seconds')
fig.x_range = Range1d(70, 130)
style(fig, 'Frequency (Hz)', 'Amplitude')
show(fig)
export_png(fig, filename = '../Images/l5_A_3.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_A_3.png'

The more cycles of a signal, the higher the certainty of the frequency. This is why we observe a linewidth of 17 Hz for the 10-cycle signal, and a linewidth of 1.7 for the 100-cycle signal.

The nyquist frequency is defined by the sample rate, which is the same for both signals. However, the number of frequency bins is defined by the number of total samples. Therefore, the range of frequency of the two signals is the same, but the one with more samples is slightly closer to the nyquist frequency due to the higher resolution.

Sine and Square Waves

[[sine_wave, sine_wave_params]] = nu.read_scope_csv('./Data/l5_B_a.csv')
sine_wave

sine_fft, freqs = nu.fft(sine_wave.mV, sine_wave.ts, 15)

fig = figure(height=400, width=600, title='Sine Wave\n Frequency Response')
fig.title.text_font_size='100pt'
fig.line(freqs/1000, sine_fft, line_width=3)
fig.x_range = Range1d(0, 11)
style(fig, 'Frequency (kHz)', 'Amplitude')
fig.xaxis.axis_label_text_font_size = '70pt'
fig.yaxis.axis_label_text_font_size = '70pt'
show(fig)
export_png(fig, filename = './troll.png')

{'record_length': [2500.0, 'Points'],
 'sample_interval': [2e-06, 's'],
 'trigger_point': [1250.0002, 'Samples']}

'/home/trevormjs/Documents/Science/APL/Lab/Lab5/troll.png'

[[square_wave, square_wave_params]] = nu.read_scope_csv('./Data/l5_B_b.csv')
square_wave

square_fft, freqs = nu.fft(square_wave.mV, square_wave.ts, 15)

fig = figure(height=400, width=600)
fig.line(freqs/1000, square_fft, line_width=3)
fig.x_range = Range1d(0, 11)
style(fig, 'Frequency (kHz)', 'Amplitude')
show(fig)
export_png(fig, filename = '../Images/l5_B_2.png')

{'record_length': [2500.0, 'Points'],
 'sample_interval': [2e-06, 's'],
 'trigger_point': [1250.0002, 'Samples']}

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_B_2.png'

Tuning Forks

[[fork, fork_config]] = nu.read_scope_csv('./Data/l5_C.csv', skiprows=200)

{'record_length': [nan, nan],
 'sample_interval': [nan, nan],
 'trigger_point': [nan, nan]}

fork.describe()

	ts	mV
count	2048.000000	2048.000000
mean	4.894000	0.019385
std	2.365404	0.095235
min	0.800000	-0.196000
25%	2.847000	-0.052000
50%	4.894000	0.016000
75%	6.941000	0.084000
max	8.988001	0.296000

3.8/np.pi/2

0.6047887837492023

from IPython.display import Audio

fig = figure(height=400, width=600)
fig.line(fork.ts, fork.mV, legend_label='Tuning Forks')
fig.line(fork.ts, .15+.15*np.cos(.6*2*np.pi*fork.ts-1.55),
         color='firebrick', legend_label='Beat estimate, cos(.6*2pi*t)', line_width=3, alpha = .5)
style(fig, 'Time (s)', 'Amplitude (mV)')
fig.legend.location = 'bottom_right'
fig.y_range = Range1d(-.37, .3)
show(fig)
export_png(fig, filename='../Images/l5_C_a.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_C_a.png'

fork_fft, freqs = nu.fft(fork.mV, fork.ts, 15)
fig = figure()
fig.line(freqs, fork_fft)
fig.x_range = Range1d(0, freqs.max())
show(fig)

[{i:[6.538*i-5.935*i]} for i in range(145, 155)]

[{145: [87.43500000000006]},
 {146: [88.03800000000001]},
 {147: [88.64100000000008]},
 {148: [89.24400000000003]},
 {149: [89.8470000000001]},
 {150: [90.45000000000016]},
 {151: [91.05300000000011]},
 {152: [91.65600000000018]},
 {153: [92.25900000000013]},
 {154: [92.8620000000002]}]

150*6.538

980.7

Whistle

[[whistle, whistle_params]] = nu.read_scope_csv('./Data/l5_D.csv')

fig = figure()
fig.line(whistle.ts, whistle.mV)
show(fig)

whistle_fft, freqs = nu.fft(whistle.mV, whistle.ts, )
fig = figure(height=300, width=600)
fig.line(freqs, whistle_fft, line_width=3)
fig.x_range = Range1d(0, freqs.max())
fig.xaxis.axis_label = 'Frequency (Hz)'
style(fig, 'Frequency (Hz)', 'Amplitude')
show(fig)
export_png(fig, filename='../Images/l5_D_1.png')

fig.x_range = Range1d(2325, freqs.max())
show(fig)
export_png(fig, filename='../Images/l5_D_1_zoomed.png')

{'record_length': [2500.0, 'Points'],
 'sample_interval': [0.00019999999495, 's'],
 'trigger_point': [1250.0001, 'Samples']}

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_D_1_zoomed.png'

[[t_whistle, whistle_params]] = nu.read_scope_csv('./Data/l5_D_1.csv')
[[a_whistle, whistle_params]] = nu.read_scope_csv('./Data/l5_D_2.csv')

{'record_length': [2500.0, 'Points'],
 'sample_interval': [0.00019999999495, 's'],
 'trigger_point': [1250.0001, 'Samples']}

{'record_length': [2500.0, 'Points'],
 'sample_interval': [0.00019999999495, 's'],
 'trigger_point': [1250.0001, 'Samples']}

a_whistle_fft, freqs = nu.fft(a_whistle.mV, a_whistle.ts, 15)
t_whistle_fft, freqs = nu.fft(t_whistle.mV, t_whistle.ts, 15)
fig = figure(height=300, width=600)
fig.line(freqs, a_whistle_fft/a_whistle_fft.max(),
         color='blue', legend_label='adrian')
fig.line(freqs, t_whistle_fft/t_whistle_fft.max(),
         color='orange', legend_label='trevor')
fig.x_range = Range1d(0, freqs.max())
fig.xaxis.axis_label = 'Frequency (Hz)'
style(fig)
show(fig)
export_png(fig, filename='../Images/l5_D_2.png')
fig.x_range = Range1d(995, 1045)
show(fig)
export_png(fig, filename='../Images/l5_D_2_zoomed.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_D_2_zoomed.png'

[[two_whistle, two_whistle_config]] = nu.read_scope_csv('./Data/TwoWhistle.csv', skiprows=2)
two_whistle

{'record_length': [2500.0, 'Points'],
 'sample_interval': [0.0002, 's'],
 'trigger_point': [1150.00005, 'Samples']}

	ts	mV
0	-0.2300	-0.10
1	-0.2298	0.22
2	-0.2296	0.20
3	-0.2294	-0.08
4	-0.2292	-0.32
...	...	...
2043	0.1786	0.10
2044	0.1788	0.26
2045	0.1790	0.02
2046	0.1792	-0.24
2047	0.1794	-0.14

2048 rows × 2 columns

fig = figure()
fig.line(two_whistle.ts, two_whistle.mV)
two_whistle_fft, freqs = nu.fft(two_whistle.mV, two_whistle.ts, magnitude=False)
two_whistle_fft *= freqs
deriv = np.fft.ifft(two_whistle_fft)
fig.line(two_whistle.ts, np.imag(deriv)/600, color = 'red', alpha = .5)
fig.line(two_whistle.ts, .3+.3*np.cos(274.5/np.pi*two_whistle.ts-.8))
show(fig)

two_whistle_fft, freqs = nu.fft(two_whistle.mV, two_whistle.ts, 15)
fig = figure(width=600, height=400)
fig.line(freqs, two_whistle_fft, line_width=1)
peak_freqs, peaks, indeces = nu.peak(two_whistle_fft,
                                     n_peaks=20,
                                     distance=100,
                                     height=.1,
                                     prominence=1,
                                     threshold=None,
#                                      prominence=None,
                                     indeces=freqs)
disp = peak_freqs[peak_freqs>0]
disp.sort()
display(disp)
fig.x_range = Range1d(0, freqs.max())
fig.xaxis.axis_label = 'Frequency (Hz)'
# style(fig, 'Frequency (Hz)','Amplitude')
show(fig)
export_png(fig, filename='../Images/l5_D_3_simultaneous_whistling.png')

array([ 395.5078125 ,  953.06396484,  995.63598633, 1011.35253906,
       1050.26245117, 1066.74194336, 1086.27319336, 1348.87695312,
       2302.39868164])

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_D_3_simultaneous_whistling.png'

Human Voice

for vowel in ['a', 'e', 'o', 'u']:
    [[whistle, whistle_params]] = nu.read_scope_csv(f'./Data/l5_E_{vowel}.csv')

#     fig = figure(title=vowel)
#     fig.line(whistle.ts, whistle.mV)
#     show(fig)

    whistle_fft, freqs = nu.fft(whistle.mV, whistle.ts, 15)

    peak_freqs, peaks, indeces = nu.peak(whistle_fft,
                                         n_peaks=30,
                                         distance=150,
                                         threshold=None,
                                         prominence=None,
                                         indeces=freqs)
    disp = peak_freqs[peak_freqs > 0]
    disp.sort()
    display(disp)

    fig = figure(title=f"The Frequency Signature of '{vowel}'",
                 height=300, width=600)
    fig.title.text_font_size='20pt'
    fig.line(freqs, np.abs(whistle_fft), line_width=3)
#     fig.scatter(peak_freqs, peaks, color = 'firebrick')
    fig.x_range = Range1d(-50, freqs.max())
    style(fig, 'Frequency (Hz)', 'Aamplitude')
    show(fig)
    export_png(fig, filename='../Images/l5_E_'+vowel+'.png')

{'record_length': [2500.0, 'Points'],
 'sample_interval': [9.9999997474e-05, 's'],
 'trigger_point': [1250.0001, 'Samples']}

array([ 157.16285558,  314.02054056,  392.75455364,  471.18339613,
        549.61223862,  628.04108111,  706.46992361,  784.8987661 ,
        863.63277918,  942.06162167, 1020.49046416, 1098.91930665,
       1177.34814914, 1255.77699163, 1334.51100472])

{'record_length': [2500.0, 'Points'],
 'sample_interval': [9.9999997474e-05, 's'],
 'trigger_point': [1250.0001, 'Samples']}

array([ 119.62687259,  186.15406194,  278.92592232,  372.30812389,
        465.38515486,  559.07252702,  651.5392168 ,  744.92141837,
       2047.99985197, 2142.60273591, 2235.67976688, 2327.23094489,
       2423.0545112 , 2794.44712331, 2888.43966606])

{'record_length': [2500.0, 'Points'],
 'sample_interval': [9.9999997474e-05, 's'],
 'trigger_point': [1250.0001, 'Samples']}

array([  99.79078403,  199.58156805,  299.37235208,  399.1631361 ,
        498.64874953,  598.74470415,  698.53548818,  798.02110161,
        897.81188564,  997.60266966, 1097.69862428, 1197.48940831,
       1297.28019233, 1397.07097636])

{'record_length': [2500.0, 'Points'],
 'sample_interval': [9.9999997474e-05, 's'],
 'trigger_point': [1250.0001, 'Samples']}

array([ 119.62687259,  176.99894414,  265.49841621,  353.69271769,
        442.19218976,  529.47097946,  618.27562213,  703.72338826,
        792.52803093,  879.80682063,  968.3062927 , 1055.89025299,
       1142.25353091, 1229.8374912 , 1407.14160594])

Musical Harmonics

[[guitar, guitar_params]] = nu.read_scope_csv(f'./Data/l5_F_guitar.csv')
[[single_string, single_string_params]] = nu.read_scope_csv(f'./Data/l5_F_single-string.csv')

{'record_length': [2500.0, 'Points'],
 'sample_interval': [9.9999997474e-05, 's'],
 'trigger_point': [1250.0001, 'Samples']}

{'record_length': [2500.0, 'Points'],
 'sample_interval': [9.9999997474e-05, 's'],
 'trigger_point': [1250.0001, 'Samples']}

instruments = pd.DataFrame({
    't': guitar.ts,
    'guitar': guitar.mV,
    '1string': single_string.mV
}).iloc[:2048]

fig = figure()
fig.line(guitar.ts, guitar.mV, legend_label = 'guitar', color = 'firebrick')
fig.line(guitar.ts, single_string.mV, legend_label = 'single_string')
# fig.line(guitar2.ts, guitar2.mV, legend_label = 'guitar2', color = 'green')
style(fig, 't (s)', 'mV')
show(fig)

import math


def frequency_to_note(frequency):
    # define constants that control the algorithm
    NOTES = ['C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#',
             'A', 'A#', 'B']  # these are the 12 notes in each octave
    OCTAVE_MULTIPLIER = 2  # going up an octave multiplies by 2
    KNOWN_NOTE_NAME, KNOWN_NOTE_OCTAVE, KNOWN_NOTE_FREQUENCY = (
        'A', 4, 440)  # A4 = 440 Hz

    # calculate the distance to the known note
    # since notes are spread evenly, going up a note will multiply by a constant
    # so we can use log to know how many times a frequency was multiplied to get from the known note to our note
    # this will give a positive integer value for notes higher than the known note, and a negative value for notes lower than it (and zero for the same note)l
    note_multiplier = OCTAVE_MULTIPLIER**(1/len(NOTES))
    frequency_relative_to_known_note = frequency / KNOWN_NOTE_FREQUENCY
    distance_from_known_note = math.log(
        frequency_relative_to_known_note, note_multiplier)

    # round to make up for floating point inaccuracies
    distance_from_known_note = round(distance_from_known_note)

    # using the distance in notes and the octave and name of the known note,
    # we can calculate the octave and name of our note
    # NOTE: the "absolute index" doesn't have any actual meaning, since it doesn't care what its zero point is. it is just useful for calculation
    known_note_index_in_octave = NOTES.index(KNOWN_NOTE_NAME)
    known_note_absolute_index = KNOWN_NOTE_OCTAVE * \
        len(NOTES) + known_note_index_in_octave
    note_absolute_index = known_note_absolute_index + distance_from_known_note
    note_octave, note_index_in_octave = note_absolute_index // len(
        NOTES), note_absolute_index % len(NOTES)
    note_name = NOTES[note_index_in_octave]
    return (note_name, note_octave)

def get_peaks_etc(fft, freqs, skipfirst=False):

    peak_freqs, peaks, indeces = nu.peak(fft,
                                         n_peaks=60,
                                         distance=200,
                                         height=2,
                                         threshold=None,
                                         prominence=None,
                                         indeces=freqs)

    peaks = np.array(peaks)
    peak_frequencies = peak_freqs[peak_freqs > 0]
    A = peaks[peak_freqs > 0]
    if skipfirst:
        min_freq_ind = peak_frequencies.argmin()
        peak_frequencies = peak_frequencies.tolist()
        A = A.tolist()
        peak_frequencies.pop(min_freq_ind)
        peak_frequencies = np.array(peak_frequencies)
        A.pop(min_freq_ind)
        A = np.array(A)

    mV = A.copy()
    A /= A.max()
    A *= 100
    note = [frequency_to_note(f) for f in peak_frequencies]
    N = np.round(
        peak_frequencies/peak_frequencies.min())

    harmonics = pd.DataFrame({'frequency': peak_frequencies,
                              'A': A,
                              'note': note,
                              'N': N,
                              'mV': mV})
    
    harmonics = harmonics.loc[
        harmonics.frequency.sort_values().index]

    return harmonics, (peak_freqs, peaks, indeces)

guitar_fft, freqs = nu.fft(guitar.mV, guitar.ts, 15)
# guitar_fft /= guitar_fft.max()
single_string_fft, freqs = nu.fft(single_string.mV, guitar.ts, 15)
# single_string_fft /= single_string_fft.max()

# guitar2_fft, freqs2 = nu.fft(guitar2.mV, guitar2.ts, 17)

fig = figure()
# guitar_fft = guitar_fft/guitar_fft.max()
fig.line(freqs,
         guitar_fft,
         legend_label='guitar',
         color='firebrick')
# single_string_fft = single_string_fft/single_string_fft.max()
fig.line(freqs,
         single_string_fft,
         legend_label='single_string')
# guitar2_fft = guitar2_fft/guitar2_fft.max()
# fig.line(freqs2,
#          guitar2_fft,
#          legend_label='guitar2',
#          color='green')

guitar_harmonics, [peak_freqs, peaks, indeces] = get_peaks_etc(
    guitar_fft, freqs, False)

display('Guitar peak frequencies', guitar_harmonics)


singlestring_harmonics, [peak_freqs, peaks, indeces] = get_peaks_etc(
    single_string_fft, freqs, False)

display('Single-String peak frequencies', singlestring_harmonics)

fig.scatter(singlestring_harmonics.frequency,
            singlestring_harmonics.mV, color='skyblue', size = 17, alpha = .75)
fig.scatter(guitar_harmonics.frequency,
            guitar_harmonics.mV, color='firebrick', size = 17, alpha = .75)
fig.x_range = Range1d(0, max(freqs)/2)
fig.y_range = Range1d(-1, 98)
style(fig)
show(fig)
export_png(fig, filename='../Images/l5_f_extra.png')

'Guitar peak frequencies'

	frequency	A	note	N	mV
4	142.209497	19.383175	(C#, 3)	1.0	18.440513
0	284.113822	100.000000	(C#, 4)	2.0	95.136698
1	425.712978	50.225799	(G#, 4)	3.0	47.783167
6	567.312133	14.280660	(C#, 5)	4.0	13.586149
5	709.826800	16.166036	(F, 5)	5.0	15.379833
3	852.951808	22.886293	(G#, 5)	6.0	21.773263
7	996.992328	7.189610	(B, 5)	7.0	6.839957
2	1140.727678	23.456165	(C#, 6)	8.0	22.315421
8	1285.378539	4.805469	(E, 6)	9.0	4.571764
9	2424.885535	2.237780	(D#, 7)	17.0	2.128950

'Single-String peak frequencies'

	frequency	A	note	N	mV
16	119.932043	6.371470	(A#, 2)	1.0	5.003408
4	277.705240	22.887233	(C#, 4)	2.0	17.972960
10	415.337178	12.551392	(G#, 4)	3.0	9.856398
8	553.579456	16.464573	(C#, 5)	5.0	12.929352
12	693.042417	10.486229	(F, 5)	6.0	8.234659
0	830.674355	100.000000	(G#, 5)	7.0	78.528321
6	969.221804	18.963050	(B, 5)	8.0	14.891365
3	1107.769254	28.495755	(C#, 6)	9.0	22.377238
13	1246.316703	9.161764	(D#, 6)	10.0	7.194580
5	1385.169323	22.583865	(F, 6)	12.0	17.734730
1	1523.716773	81.466033	(G, 6)	13.0	63.973908
11	1661.959051	12.131977	(G#, 6)	14.0	9.527038
9	1800.811671	16.103885	(A, 6)	15.0	12.646111
2	1938.748780	35.881801	(B, 6)	16.0	28.177376
7	2077.601400	18.392281	(C, 7)	17.0	14.443150
15	2215.538508	6.591576	(C#, 7)	18.0	5.176254
14	2493.243748	8.053837	(D#, 7)	21.0	6.324543
17	3047.433545	3.043708	(G, 7)	25.0	2.390173

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_f_extra.png'

from bokeh.models import LinearAxis, tickers

tickers.CategoricalTicker()
#     [f'{note[0]} {note[1]}' for note in singlestring_harmonics.note])

CategoricalTicker(

id = '107922', …)

js_event_callbacks = {},

js_property_callbacks = {},

name = None,

subscribed_events = [],

tags = [])

singlestring_harmonics[['N','note']].T.to_dict()

{4: {'N': 1.0, 'note': ('C#', 4)},
 10: {'N': 1.0, 'note': ('G#', 4)},
 8: {'N': 2.0, 'note': ('C#', 5)},
 12: {'N': 2.0, 'note': ('F', 5)},
 0: {'N': 3.0, 'note': ('G#', 5)},
 6: {'N': 3.0, 'note': ('B', 5)},
 3: {'N': 4.0, 'note': ('C#', 6)},
 13: {'N': 4.0, 'note': ('D#', 6)},
 5: {'N': 5.0, 'note': ('F', 6)},
 1: {'N': 5.0, 'note': ('G', 6)},
 11: {'N': 6.0, 'note': ('G#', 6)},
 9: {'N': 6.0, 'note': ('A', 6)},
 2: {'N': 7.0, 'note': ('B', 6)},
 7: {'N': 7.0, 'note': ('C', 7)},
 15: {'N': 8.0, 'note': ('C#', 7)},
 14: {'N': 9.0, 'note': ('D#', 7)},
 16: {'N': 11.0, 'note': ('G', 7)}}

labels = {int(N): f'{note[0]} {note[1]}' for N, note in zip(
    singlestring_harmonics.N, singlestring_harmonics.note)}

labels.update({int(N): f'{note[0]} {note[1]}' for N, note in zip(
    guitar_harmonics.N, guitar_harmonics.note)})

fig = figure(width=800, height=500)
fig.scatter(singlestring_harmonics.N, (singlestring_harmonics.A),
            legend_label='singlestring', size=10)
fig.scatter(guitar_harmonics.N, (guitar_harmonics.A),
            legend_label='guitar', color='firebrick', size=10)
style(fig, 'N Harmonic', 'Scaled Amplitude')
ax2 = LinearAxis(axis_label='Note',)
ax2.ticker = list(labels.keys())
ax2.major_label_overrides = labels
ax2.major_label_orientation = np.pi/4
ax2.major_label_text_font_size = '14pt'
ax2.axis_label_text_font_size = '20pt'
# ax2.major_label_orientation = "vertical"
fig.add_layout(ax2, 'above')
fig.xgrid.visible = True
fig.xgrid.minor_grid_line_color = 'navy'
fig.xgrid.minor_grid_line_alpha = 0.6
fig.xgrid.grid_line_color = 'navy'
fig.xgrid.grid_line_alpha = 0.6
fig.x_range = Range1d(.1, 22.4)
fig.y_range = Range1d(-0.1, 102)
show(fig)
export_png(fig, filename='../Images/l5_f.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_f.png'

Optional

y = sin(2pi100x) from x = 0 to 0.1 seconds, using 100 points and only 10 points

x1 = np.linspace(0, .1, 100)
x2 = np.linspace(0, .1, 10)
x3 = np.linspace(0, .1, 20)
x4 = np.linspace(0, .1, 19)

y1 = np.sin(2*np.pi*100*x1)
y2 = np.sin(2*np.pi*100*x2)
y3 = np.sin(2*np.pi*100*x3)
y4 = np.sin(2*np.pi*100*x4)

fig = figure(height=400, width=600)
fig.line(x1, y1, legend_label='100', line_width=3, alpha=.7)
fig.line(x3, y3, legend_label='20', color='green', line_width=3, alpha=.7)
fig.line(x4, y4, legend_label='19', color='purple', line_width=3, alpha=.7)
fig.line(x2, y2, legend_label='10', color='firebrick', line_width=3, alpha=.7)
fig.legend.orientation = 'horizontal'
fig.legend.title = 'N Samples'
fig.legend.title_text_font_size = '18pt'
fig.y_range = Range1d(-1.05, 2)
fig.yaxis.ticker=[-1,0,1]
style(fig, 'Time (s)', 'y(t)')
show(fig)
export_png(fig, filename='../Images/l5_optional.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_optional.png'

fft1, freqs1 = nu.fft(y1, x1)

fft2, freqs2 = nu.fft(y2, x2)
fig = figure()
fig.line(freqs1, fft1, legend_label = 'signal1')
fig.line(freqs2, fft2, legend_label = 'signal2', color = 'firebrick')
show(fig)

import librosa

from IPython.display import Image

Image('../Images/l5_optional_flute.jpg')

flute, sample_rate = librosa.load('./Data/cardboard_flute.mp3')

/home/trevormjs/anaconda3/envs/conda_env/lib/python3.8/site-packages/librosa/core/audio.py:165: UserWarning:

PySoundFile failed. Trying audioread instead.

flute = pd.DataFrame({'ts': np.arange(0, len(flute))/sample_rate,
                     'mV': flute})

flute.shape

(41472, 2)

import librosa

from IPython.display import Image

Image('../Images/l5_optional_flute.jpg')

flute, sample_rate = librosa.load('./Data/cardboard_flute.mp3')

/home/trevormjs/anaconda3/envs/conda_env/lib/python3.8/site-packages/librosa/core/audio.py:165: UserWarning:

PySoundFile failed. Trying audioread instead.

flute = pd.DataFrame({'ts': np.arange(0, len(flute))/sample_rate,
                     'mV': flute})

flute.shape

(41472, 2)

fig = figure()
fig.line(flute.ts, flute.mV)
show(fig)

flute_fft, flute_freqs = nu.fft(flute.mV[1000:3048], flute.ts, 15)
flute_harmonics, _ = get_peaks_etc(
    flute_fft, flute_freqs, True)
# display(flute_harmonics)
flute_harmonics = flute_harmonics.loc[
    (flute_harmonics.frequency > 200) &
    (flute_harmonics.mV > 6)
]
fig = figure()
fig.line(flute_freqs/1000, flute_fft, legend_label='FFT')
fig.scatter(flute_harmonics.frequency/1000, flute_harmonics.mV,
            color='firebrick', legend_label='Harmonics')
fig.x_range = Range1d(0, max(flute_freqs)/1000)
style(fig, 'Frequency (kHz)', 'Amplitude')
show(fig)

labels = {int(N): f'{note[0]} {note[1]}' for N, note in zip(
    flute_harmonics.N, flute_harmonics.note)}

fig = figure(width=800, height=500)
fig.scatter(flute_harmonics.N, (flute_harmonics.A),
            legend_label='flute?', size=10)
style(fig, 'N Harmonic', 'Scaled Amplitude')
ax2 = LinearAxis(axis_label='Note',)
ax2.ticker = list(labels.keys())
ax2.major_label_overrides = labels
ax2.major_label_orientation = np.pi/4
ax2.major_label_text_font_size = '14pt'
ax2.axis_label_text_font_size = '20pt'
# ax2.major_label_orientation = "vertical"
fig.add_layout(ax2, 'above')
fig.xgrid.visible = True
fig.xgrid.minor_grid_line_color = 'navy'
fig.xgrid.minor_grid_line_alpha = 0.6
fig.xgrid.grid_line_color = 'navy'
fig.xgrid.grid_line_alpha = 0.6
show(fig)

fig = figure()
fig.line(flute.ts, flute.mV)
show(fig)

flute_fft, flute_freqs = nu.fft(flute.mV[1000:3048], flute.ts, 15)
flute_harmonics, _ = get_peaks_etc(
    flute_fft, flute_freqs, True)
# display(flute_harmonics)
flute_harmonics = flute_harmonics.loc[
    (flute_harmonics.frequency > 200) &
    (flute_harmonics.mV > 6)
]
fig = figure(width=600, height=400)
fig.line(flute_freqs/1000, flute_fft, legend_label='FFT')
fig.scatter(flute_harmonics.frequency/1000, flute_harmonics.mV,
            color='firebrick', legend_label='Harmonics')
fig.x_range = Range1d(0, max(flute_freqs)/1000)
style(fig, 'Frequency (kHz)', 'Amplitude')
show(fig)
export_png(fig, filename='../Images/l5_optional_flute_fourier.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_optional_flute_fourier.png'

labels = {int(N): f'{note[0]} {note[1]}' for N, note in zip(
    flute_harmonics.N, flute_harmonics.note)}

fig = figure(width=800, height=500)
fig.scatter(flute_harmonics.N, (flute_harmonics.A),
            legend_label='flute?', size=10)
style(fig, 'N Harmonic', 'Scaled Amplitude')
ax2 = LinearAxis(axis_label='Note',)
ax2.ticker = list(labels.keys())
ax2.major_label_overrides = labels
ax2.major_label_orientation = np.pi/4
ax2.major_label_text_font_size = '14pt'
ax2.axis_label_text_font_size = '20pt'
# ax2.major_label_orientation = "vertical"
fig.add_layout(ax2, 'above')
fig.xgrid.visible = True
fig.xgrid.minor_grid_line_color = 'navy'
fig.xgrid.minor_grid_line_alpha = 0.6
fig.xgrid.grid_line_color = 'navy'
fig.xgrid.grid_line_alpha = 0.6
fig.xgrid.ticker = list(range(11))
fig.xaxis.ticker = list(range(11))
show(fig)
export_png(fig, filename='../Images/l5_optional_flute_harmonics.png')

'/home/trevormjs/Documents/Science/APL/Lab/Images/l5_optional_flute_harmonics.png'